Constraining Pyrite Activity in Shale

ABSTRACT

Degeneration of shale caused by oxygen in aqueous drilling, fracturing and completion fluids is minimized by introducing imidazolines modified so that they will be attracted efficiently to pyrites in the shale, thereby forming a protective coating on the pyrites. Inhibiting oxidation of the pyrites sharply reduces physical degradation of the shale in the presence of drilling, fracturing and completion fluids carrying oxygen. The imidazoline is an ionic salt or a beatine.

TECHNICAL FIELD

In the recovery of hydrocarbons from the earth, degeneration of shale caused by oxygen in aqueous drilling, fracturing and completion fluids is minimized by introducing imidazolines modified as betaines or ionic salts so that they will be attracted efficiently to pyrites in the shale, thereby forming a protective coating on the pyrites. Inhibiting oxidation of the pyrites sharply reduces physical degradation of the shale in the presence of drilling, fracturing and completion fluids carrying oxygen.

BACKGROUND OF THE INVENTION

We have observed that, because of the normal operation of the pumps and other equipment used to place aqueous drilling fluids, workover fluids and fracturing fluids in wells, it is almost impossible to avoid including significant amounts of air in the fluid. While some of the oxygen may be dissolved, most of it remains in gaseous form. Oxygen in the air carried into the formation oxidizes the iron pyrites present on the surface of the shale in contact with the drilling or fracturing fluid. Chemical oxidizers in the form of gel breakers and biocides can also introduce oxygen into the fluid. When sulfur is released from the iron pyrite through oxidation of the iron pyrite, it tends to combine with other multivalent metals present in the formation, causing highly undesirable compounds to enter the produced fluids. Oxidation of iron pyrite not only results in troublesome sulfates of metals such as barium, calcium, and strontium, but also can generate iron oxides which will precipitate in the circulating fluid, causing deposits in piping, pumps and machinery, and even find its way into the produced hydrocarbons. Even very small amounts of iron in the oil or gas can be detrimental to catalysis and other processing steps for the hydrocarbon product. Moreover, after oxidation of iron pyrite, the mobility of both the iron and the sulfur from the previously situated iron pyrite is physically destructive to the shale.

Oxygen is almost always present in drilling, fracturing, and other aqueous well treatment fluids in amounts of at least 1%, generally in the range of 3% to 10% by volume; the actual volume of gaseous oxygen, and the portion dissolved, are functions of the pressure and temperature and to an extent the turbulence of the flow.

In the past, oxygen scavengers have been used to try to reduce the amount of dissolved oxygen that will react downhole. The most common oxygen scavengers, however, ammonium bisulfite and sodium bisulfite, both introduce free sulfate to the reservoir, where there is typically an excess of barium, strontium and calcium ionically bound to the substrate. Depending on their solubility constants and the common ion effect, the barium, strontium and calcium will more or less readily combine with the free sulfate to create water-insoluble scale.

It has recently become clear that virtually all shales encountered in drilling and fracturing operations, either in the recovery of oil or of natural gas, contain from 0.1% to 15% by volume iron pyrite distributed throughout. See, for example, John Kiefer and Warren H. Anderson “Foundation Problems and Pyrite Oxidation in the Chattanooga (Ohio) Shale, Estill County, Kentucky, Kentucky Geological Survey, University of Kentucky. Kiefer and Anderson have shown the detrimental effects of pyrite oxidation on the foundation of a building. When drilling through shale or an extended reach lateral (a horizontal wellbore in the shale that reaches out from the vertical wellbore) in the shale, similar shale stability problems are encountered. Wellbore stability in the shale is critical for successful drilling into any shale formation. If the shale loses its structural strength, the wellbore can collapse around the drill pipe, and in severe cases the hole being drilled must be abandoned along with the downhole equipment and the drill pipe. Because of ground stress, the action of water used in the drilling process, and wellbore pressures, shale stability problems are significantly greater in hydrocarbon recovery compared to the foundation problems encountered by Kiefer and Anderson. A typical reaction between pyrite and water is presented as 2FeS₂+3H₂O+3CaCO₃+6O₂→FeCa(SO₄)+CO₂+Fe. This paper deals with disintegration of shale around the foundation of a building, and thus does not involve a drilling or fracturing fluid, but the effects of oxygen studied is significant for drilling and fracturing operations. In part because of the abundance of pyrite in the shale, the described decomposition of the iron pyrite contributes significantly to the undesirable structural disintegration of the shale which plagues hydrocarbon recovery operations throughout the industry. Oxygen reacts both with iron and sulfur, causing rapid disintegration of the pyrite.

Since oxygen, both dissolved and undissolved (which together we call “free oxygen”), in the drilling or fracturing fluid is unavoidable, the damage caused by oxidation of iron pyrite alone can be very significant, resulting not only in the production of undesired multivalent metal compounds, but also, because the iron sulfide is a significant part of the shale, its molecular disruption significantly weakens the structure of the shale, exacerbating any independent hydration effects.

There is a need to cure the problem of formation damage following from the oxidation of iron pyrite in shale.

As will be seen below, a group of imidazoline derivatives has been found effective for constraining the degradation of shale and clay by inhibiting the oxidation of iron pyrite in the shale and clay. The reader may therefore be interested in reviewing the 1958 patent to Bohor et al, U.S. Pat. No. 3,389,750, describing the use of high molecular weight imidazolines to control formation damage in waterflooding practices. The Bohor patent lists some imidazoline derivatives, such as 1-hydroxyethyl-2-hexadecenyl imidazoline; 1-diethyldiamino-2-pentadecenyl imidazoline, 1-triethyltriamino-2-heneico senyl imidazoline, 1-hydroxypropyl-2-octadecenyl imidazoline, and 1-hydroxypropyl-2-pentadecenyl imidazoline. Generally, these materials can be made by the reaction of an ethylene polyamine with a carboxylic acid. Imidazolines within a general imidazoline structure where the 1 position is occupied by a group of the formula —(CH₂CH₂NH)_(m)C₂H₄NH₂ and the 2 position is occupied by a hydrocarbon group derived from a straight chain fatty acid and containing from about 14 to about 22 carbon atoms, and a number of other imidazolines are attributed to DeGroote et al in U.S. Pat. No. 3,049,492, who recommend them for controlling sulfate-reducing bacteria in oil recovery methods. Even earlier, White et al, in U.S. Pat. No. 2,568,876, described the use of various imidazolines, for example the reaction products of oleic acid with tetraethylenepentamine, and, separately with diethylenetriamine, as corrosion inhibitors.

SUMMARY OF THE INVENTION

Our method involves the formation of a protective hydrophobic coating on the iron pyrite exposed to possible contact with a drilling fluid or fracturing fluid unavoidably containing infused oxygen. The protective coating is accomplished by deploying imidazoline groups on the iron of the pyrite exposed to the fluid. Because the imidazoline group has two nitrogens, at least one of which is further polarized by modifying groups which we place on it, it is readily attracted to, and by, the iron in the pyrite. Further, the imidazoline group has a relatively flat configuration, which enhances the attraction. But imidazoline by itself—unmodified—is not water soluble or otherwise amenable to placement on a remote shale surface.

We have found that if the imidazoline is modified in the manner of our invention, it can not only be dispersed in a manner that its deposition on the pyrite is assured, but it will also form a hydrophobic layer on the shale, further protecting the shale from water and oxygen damage. It is important in our invention that the mechanism for inhibiting shale disintegration is the shielding of iron pyrites from oxygen in the water. While water hydration of other portions of the shale is inhibited by our protective coating, the main effect of our invention is the prevention of oxidation of iron pyrites by oxygen transported by and infused into the drilling or fracturing fluid when it is pumped. The sulfur in the pyrite is thus constrained from combining with other multivalent metals such a barium, strontium and calcium. And, iron oxides are not created to cause problems in the system. The shale is stabilized because oxygen is not permitted to contact the plentiful iron pyrite.

The hydrophobic coating we construct inhibits the contact of pyrite deposits by the fracturing fluid, thus preventing contact of the pyrite with oxygen carried by the fluid, thus preventing the formation of undesirable sulfates and iron compounds. The pyrite is retained more or less in its original form during drilling, and the shale is also protected against damage by the water. Fracturing fluids are thus able to perform their primary functions of fracturing and transporting proppant without undue concern about the degeneration of the shale formation and the gratuitous generation of di- and trimetallic sulfates or itinerant iron compounds. Drilling fluids are able to perform their primary function of transporting drill cuttings to the surface, also without fear of damaging the shale surrounding the well.

Unmodified imidazoline is substantially water-insoluble and accordingly is difficult to use in an aqueous drilling or fracturing fluid. Imidazoline placed in water will simply form into hydrophobic ball-like bodies and will resist placement anywhere.

Since imidazoline is not soluble in water, it does not behave as an ionic salt. By carefully selecting the reactants for making our imidazoline derivatives, we create ionic salts from these entirely organic materials. The modifications we introduce to the imidazoline molecule are designed to render it dispersible rather than soluble.

In particular, we can accomplish our objective of protecting the shale by including in a drilling fluid, a fracturing fluid, or other well treatment fluid a pyrite control additive comprising (a) an imidazoline of the formula

-   -   where R¹ is H or a linear alkyl, or mono- or diunsaturated alkyl         or alkylene group of 1-22 carbon atoms, R² is         —(CH₂CH₂NH)_(n)CH₂CH₂R³ where n is 0-5, and R³ is either OH or         NH₂, and (b) a linear carboxylic acid having from 1 to 22 carbon         atoms in a molar ration of (a) to (b) of 1:10 to 10:1.

DETAILED DESCRIPTION OF THE INVENTION

To demonstrate the vulnerability of pyrite-containing shale (virtually all hydrocarbon-bearing shale) to dissolved oxygen, experiments were run comparing the contents of various constituents in oxygenated and deoxygenated water after rinsing samples of shale. Shale samples were ground in air for the oxygenated water runs and in argon for the deoxygenated runs. Each rinse represents 60 milliliters of the designated water having been passed through 60 grams of sample.

TABLE I Ox Ox Ox Ox Ox Ox Ox Ox Ox Water rinse 1 rinse 2 rinse 3 rinse 4 rinse 5 rinse 6 rinse 7 rinse 8 Iron 3.98 7.57 12.4 6.64 10.4 8.95 5.98 5.72 3.83 Magnesium 1.47 1.77 2.11 1.74 1.85 1.85 1.26 1.27 0.914 Barium 0.656 1.06 5.04 0.863 3.12 1.6 1.39 0.821 0.697 Potassium 31.1 29 35.5 44.5 29.1 26.2 22.5 23.4 22.8 Sodium 1200 494 278 192 94.3 60 41.1 29.5 20.6 Strontium 3.08 1.22 1.09 1.17 0.644 0.56 0.488 0.563 0.623 Silica 26.4 45.2 48.5 47.4 58.1 59 34.4 35.7 21.8 Calcium 20 12 14.9 12.5 11.3 9.4 8.32 8.37 9.15 Aluminum 6.39 12.3 13.7 13.5 17.4 17.8 10.3 10.9 6.38 Chloride 1820 790 537 444 203 126 102 92.6 89.4 Sulfate 214 78.6 37.8 24.2 22.7 19.3 15.6 16.4 15.6 Total 232 192 169 145 155 138 126 110 100 Alkalinity Deox Deox Deox Deox Deox Deox Deox Deox Deox Water Rinse 1 Rinse 2 Rinse 3 Rinse 4 Rinse 5 Rinse 6 Rinse 7 Rinse 8 Iron 0.422 0.483 0.331 0.867 0.407 0.208 0.306 0.402 0.434 Magnesium 0.231 0.33 0.539 0.813 1.02 1.78 2.25 1.21 0.934 Barium 0.103 0.136 0.188 0.325 0.382 0.609 0.732 0.328 0.235 Potassium 7.52 10.9 16 28.3 33.3 50.4 57.8 34.8 26.8 Sodium 543 338 247 172 118 70 42.7 20.7 11.4 Strontium 0.653 0.533 0.709 1.12 1.42 2.24 2.67 1.18 0.811 Silica 10.7 7.23 9.03 10.1 5.39 3.56 3.46 5.74 6.64 Calcium 5.17 5.8 6.61 11.6 13.4 22.7 27.1 13.8 10 Aluminum 2.13 1.46 2.18 3.23 1.12 0.497 0.52 1.3 1.7 Chloride 676 492 440 395 386 381 381 184 114 Sulfate 43.1 19.5 11 7.9 7 5.9 6.9 8.4 8.2

Results are shown in parts per million of the constituents in Table I. Notably, the iron content of the deoxygenated rinse water is consistently substantially lower than that of the oxygen-containing water. The shale apparently absorbs sulfate, which appears to be generated when the pyrite is oxygenated.

A class of compositions encompassed within General Formula I, in an aqueous carrier, may be said to have the structural formula

where R¹ and n are as defined above, and y is 0 or an integer from 1 to 21. We refer to this charge separated class of materials as ionic salts. As the structural formula implies, the ionic salt of Formula II is in a molar ratio of 1:1, but an excess of either component (a) or (b) is not undesirable—rather, it can sometimes further facilitate the dispersion of the pyrite control additive in the well treatment fluid.

Another class of materials within General Formula I may be said to have the structural formula

Where R¹, n and y are as defined above. In this case the dissociated carboxylic acid has a charge separation orientation with the nitrogen in the 1 position in the imidazoline ring. As we depict this nitrogen in the (+) onium form, the dissociated complex is called a betaine, although the more generic term “ionic salt” is still applicable.

A specific ionic salt within Formula II useful in our invention is made by first conducting the following reaction:

Water is also produced. In this illustration, the fatty acid may be oleic acid. Oleic acid is a major constituent of tall oil, sometimes called tall oil fatty acid, or TOFA, which may be used instead. Tall oil includes linoleic acid and palmitic acid, which also could be used by themselves. Thus the long chain fatty acid may be saturated or unsaturated; linoleic acid is diunsaturated.

To this material, which may be called 1-ethylamino 2-oleyl imidazoline, is added acetic acid in a molar ratio of 1:10 to 10:1.

If the diethylene triamine is replaced with triethylene tetramine and the oleic acid is replaced with butyric acid, the resultant imidazoline product is

The polyamine may have from 3 to 6 amine groups, as implied by General Formula I. The carboxylic acid forming the ionic salt at the terminus of the 1-position may be formic or any acid having up to 20 carbon atoms.

Generally, the reactions of carboxylic acids and polyamines to make imidazolines are well known. Variations and conditions for the reactions may be found, for example, in White et al U.S. Pat. No. 2,568,876, which is hereby incorporated entirely and specifically herein by reference. Monocarboxylic acids which may be used include (as examples) formic acid; acetic acid; propionic acid; butyric acid; pentanoic (valeric) acid; hexanoic acid; octanoic (caprylic) acid; decanoic acid; dodecanoic (lauric) acid; tetradecanoic (myristic) acid; heptadecanoic acid; octadecanoic (stearic) acid; oleic acid, linoleic acid; linolenic acid, palmitic acid, and docosanoic (behenic) acid.

A modified roller oven test was conducted to determine the effect of our additive on the contents of various components of the effluents from the samples. As is known in the art, the roller oven shale stability test simulates the circulation effect of the fluid around ground rock particles over a period of 16-24 hours at a desired temperature and studies the reduction of particle size due to mechanical attrition and reaction of shale particles with the reacting fluids.

In the modified API RP 13i procedure used in these studies, the shale was ground to a particle size less than 2 mm (10 mesh) and larger than 0.425 mm (40 mesh). These particles were split equally using a spinning Riffler, then distributed equally into 10 gm samples. The number of samples depends on the number of fluids to be tested. The weighed sample was placed in a glass bottle along with 50 ml of fluid and allowed to roll in a roller oven at a desired temperature. Following the aging, the samples were screened through a 70 mesh screen (0.269 mm) and washed with fresh water prior to drying and reweighing.

FIG. 1 shows the results of the modified roller oven tests, comparing two materials of our invention to other materials. The material designated “118” is Formula IV above made with tall oil (arbitrarily C₁₇, a major constituent) neutralized with acetic acid to achieve a pH of 8.5, and the material designated “259” is Formula II (also made with tall oil) above neutralized with butyric acid, also brought to a pH of 8.5. The term “gpt” means gallons per 1000 gallons. Percentages are by weight in water.

Table 2 is a comparison of the analysis of effluent from samples using fresh water and our additive (“118”) in the same water. Neither the fresh water nor the water containing “118” was deoxygenated. The composition of “118” was as stated in the next previous paragraph, having a pH of 8.5. Based on the amount of sample passed through the 70 mesh screen, the “118” treated samples were far more stable than the untreated ones.

TABLE 2 Sample ID: 118 RO Effluent Parameter Ratio - Result Units Result Units 118:Fresh Aluminum 14000 μg/L 14 mg/L 0.17 Barium 1520 μg/L 1.52 mg/L 0.47 Calcium 72700 μg/L 72.7 mg/L 0.40 Iron 31000 μg/L 31 mg/L 0.22 Potassium 21000 μg/L 21 mg/L 0.63 Magnesium* 13300 μg/L 13.3 mg/L 0.32 Sodium 145000 μg/L 145 mg/L 0.97 Silica 31000 μg/L 31 mg/L 0.17 Strontium 1400 μg/L 1.4 mg/L 0.98 Chloride 145 mg/L 1.00 Sulfate 15.2 mg/L 0.42 Sample ID: Fresh Water RO Effluent Parameter Result Units Result Units Aluminum 82300 μg/L 82.3 mg/L Barium 3210 μg/L 3.21 mg/L Calcium 182000 μg/L 182 mg/L Iron 141000 μg/L 141 mg/L Potassium 33400 μg/L 33.4 mg/L Magnesium 41600 μg/L 41.6 mg/L Sodium 150000 μg/L 150 mg/L Silica 182000 μg/L 182 mg/L Strontium 1430 μg/L 1.43 mg/L Chloride 145 mg/L Sulfate 36.5 mg/L *Result less than reporting limit

Note the iron content of the “118” containing water was 22% of the effluent using fresh water; also the sulfate content was 42%.

An aqueous drilling fluid for use in our invention will comprise water, 0.1% to 5% by weight of an imidazoline of general formula I, and a small amount (0.1% to 0.5% by weight) of a viscosity-enhancing (Bingham plastic inducing) polymer. Examples of Bingham plastic inducing polymers are xanthan gum, hydroethylcellulose, carboxymethyl guar, starches, carboxymethylcellulose and/or other natural or synthetic polymers and their derivatives. The Bingham plastic (viscosity-enhancing) additive provides gel strength to assist in removing drill cuttings and other solids in the fluid

In addition to 0.1% to 5% by weight imidazoline of the General Formula I, an aqueous fracturing fluid will comprise water and up to 24 pounds per gallon (0.1 to 24 ppg or more) of a proppant such as sand or any other effective proppant for assuring the formation fractures remain open, and frequently a viscosifying agent.

Generally, lower molecular weight modified imidazolines are more useful for fracturing fluids as they are better able to penetrate and contact the large surface areas opened up during the fracturing process. Generally, the higher molecular weight modified imidazolines are more useful in drilling fluids, where the longer alkyl or alkenyl chains will contribute a lubricity effect in addition to the shale protective effect. However, it should be understood that shale compositions vary considerably as do the conditions of any well operation, and we do not intend to be limited to high or low molecular weight compositions for any particular type of operation, although some may be more effective, as a matter of degree, than others in particular circumstances.

The lubricity effect was demonstrated by comparing two materials of our invention to tap water and an oil based mud sample, in a Baroid Lubricity Meter. The Baroid Lubricity Meter is a device that uses a rotating metal ring against a fixed block. The test sample is placed in a metal bowl, then used to immerse the metal ring and the block. After turning on the machine motor and adjusting the rotation to 60 rpm, a torque meter is used to apply a load of 150 lbs-inch to the rotating metal ring.

Readings from the torque meter are taken after one, three and five minutes. The average of the torque meter readings is then used to calculate the lubricity coefficient. Here, the samples were tested using metal to metal and metal to sandstone contacts. Results are presented in Tables 3 and 4:

TABLE 3 Metal to Metal Lubricity Coefficients Sample Lubricity Coefficient Tap Water 0.283 Oil Based Mud #2 0.145 Formula A 0.084 Formula B 0.088

TABLE 4 Metal to Sandstone Lubricity Coefficients Sample Lubricity Coefficient Tap Water 0.279 Oil Based Mud #2 0.128 Formula A 0.073 Formula B 0.075

Formulas A and B were two different samples of a proposed mud containing 1% by weight oleyl imidazoline in water also containing 3% by weight potassium chloride and weighted with 10 pounds per gallon barite. The performance of Formulas A and B were considered excellent. 

1. A pyrite control additive for drilling and fracturing fluids for inhibiting oxidation of iron pyrite in shale comprising (a) an imidazoline of the formula

where R¹ is H or a linear alkyl, or monounsaturated or diunsaturated alkyl or alkenyl group of 1-22 carbon atoms, R² is —(CH₂CH₂NH)_(n)CH₂CH₂R³ where n is 0-5, and R³ is either OH or NH₂, and (b) a linear monocarboxylic acid having from 1 to 22 carbon atoms in a molar ratio of (a) to (b) of 1:10 to 10:1.
 2. Additive of claim 1 wherein R¹ comprises the residue of oleic acid.
 3. Additive of claim 1 wherein said linear monocarboxylic acid (b) comprises acetic acid.
 4. Additive of claim 1 wherein R¹ comprises a residue of carboxylic acid having 16-19 carbon atoms and carboxylic acid (b) comprises acetic acid.
 5. Additive of claim 1 wherein R¹ comprises a residue of a carboxylic acid having 16-19 carbon atoms and carboxylic acid (b) comprises butyric acid.
 6. An aqueous drilling fluid for drilling wells comprising water, 0.1% to 5% by weight of a pyrite control additive of claim 1, and 0.1% to 2% by weight of a Bingham plastic inducing polymer.
 7. An aqueous drilling fluid for drilling wells comprising water, 0.1% to 5% by weight of a pyrite control additive of claim 2, and 0.1% to 2% by weight of a Bingham plastic inducing polymer.
 8. An aqueous drilling fluid for drilling wells comprising water, 0.1% to 5% by weight of a pyrite control additive of claim 3, and 0.1% to 2% by weight of a Bingham plastic inducing polymer.
 9. An aqueous drilling fluid for drilling wells comprising water, 0.1% to 5% by weight of a pyrite control additive of claim 4, and 0.1% to 2% by weight of a Bingham plastic inducing polymer.
 10. An aqueous drilling fluid for drilling wells comprising water, 0.1% to 5% by weight of a pyrite control additive of claim 5, and 0.1% to 2% by weight of a Bingham plastic inducing polymer.
 11. An aqueous fracturing fluid for fracturing earth formations comprising water, 0.1% to 5% by weight of a pyrite control additive of claim 1, and a proppant in an amount effective to prop open fractures generated in said earth formations.
 12. An aqueous fracturing fluid for fracturing earth formations comprising water, 0.1% to 5% by weight of a pyrite control additive of claim 2, and 0.1 to 24 pounds of a proppant per gallon of said fracturing fluid.
 13. An aqueous fracturing fluid for fracturing earth formations comprising water, 0.1% to 5% by weight of a pyrite control additive of claim 3, and up to 24 pounds per gallon of a proppant.
 14. An aqueous fracturing fluid for fracturing earth formations comprising water, 0.1% to 5% by weight of a pyrite control additive of claim 4, and up to 24 pounds of a proppant per gallon of said fracturing fluid.
 15. An aqueous fracturing fluid for fracturing earth formations comprising water, 0.1% to 5% by weight of a pyrite control additive of claim 5, and an amount of a proppant effective to prop open fractures generated in said earth formations by said fracturing fluid.
 16. Method of inhibiting the oxidation of iron pyrite present in shale by free oxygen in an aqueous well treatment fluid in contact with said shale comprising adding to said well treatment fluid an imidazoline ionic salt of the formula

where R is a residue of a carboxylic acid containing 1 to 23 carbon atoms, n is 0 to 5, and y is 0 to 21, in an amount effective to form a protective layer on iron pyrite in said shale.
 17. Method of claim 16 wherein n is 1 and y is
 0. 18. Method of claim 16 wherein R is derived from tall oil.
 19. Method of inhibiting the oxidation of iron pyrite present in shale by free oxygen in an aqueous well treatment fluid comprising adding to said well treatment fluid a composition comprising (a) an imidazoline of the formula

where R¹ is H or a linear alkyl, or monounsaturated or diunsaturated alkyl or alkenyl group of 1-22 carbon atoms and (b) a linear monocarboxylic acid having 1 to 22 carbon atoms in a molar ratio of (a) to (b) of 1:10 to 10:1, said composition (a) and (b) being added to said well treatment fluid in an amount effective to form a protective coating on said shale.
 20. Method of claim 19 wherein at least a portion of said coating of said imidazoline (a) and said carboxylic acid (b) is an imidazoline betaine of the formula

where y is 0-5. 